ges. sin(nn2) Prove, using the e - N definition, that this sequence Define the sequence {xn} by Xn 8.

Find the limit of the following sequence or determine that the sequence diverges. {((-1)n)/(n)}

3. Show that if (xn) is a convergent sequence in ₁, then it is also a convergent sequence with respect to the || ||. Give an example of a sequence to show that the converse of this statement is not true.

Suppose that {xn} is a convergent sequence and {yn} is a sequence such that for any e > 0 there exists M(e) EN such that |æn – Yn| M(e). Is the sequence {yn} convergent?